Infidelity [1]} generalizes the previous metrics from perturbation by masking to general perturbations. This is done by comparing the difference in output after an arbitrary perturbation with the dot product of the perturbation vector \(\mathbf {I}\)  and the attribution map \(\mathbf {e}\) .
The perturbation vector is a random variable \(\mathbf {I} \in \mathbb {R}^d\)  with probability measure \(\mu _\mathbf {I}\) . The infidelity of an attribution map \(\mathbf {e}\)  for an input sample \(\mathbf {x}\)  and class \(c\)  is then defined as follows:
\(INFD(\mathbf {x}, m, \mathbf {e}, c) &= \mathbb {E}_{\mathbf {I} \sim \mu _\mathbf {I}} \left[ (\beta \mathbf {I}^T \mathbf {e} - (m(\mathbf {x})_c - m(\mathbf {x} - \mathbf {I})_c))^2 \right]\\\beta &= \frac{\mathbb {E}_{I \sim \mu _I} [ I^T \mathbf {e} (m(\mathbf {x})_c - m(\mathbf {x} - \mathbf {I})_c) ]}{\mathbb {E}_{I \sim \mu _I} [ (I^T \mathbf {e})^2 ]}\) 
